I don't know that there is a pat answer. My boundaries/limits change from coach to coach, player to player, day to day, game to game, even from inning to inning. In reality my limits are all pretty even across the board but there are times, and people, that I am more tolerant with.
In general, when the coach steps beyond the questioning attitude to a confrontational or demanding attitude (that I'm not doing the job he wants me to do - call his strikes, call his outs/safes, etc.) he has one foot on the way out of the game. I'm usually quiet at this stage and require the coach to put the other foot in the grave before I would send him. If a coach is inciting players or fans to adopt this questioning, challenging attitude, he has one foot in the grave too.
BUT IT TAKES TWO TO TANGO/tangle. Often it is the umpire's attitude that can either calm the situation of exacerbate it to a higher level creating a situation that requires, or is best alleviated by an ejection. So... in general, I feel the umpire often helps cause the ejection by taking a defensive stance rather than a matter-of-fact approach (this is what I saw, this is what I called).
If I am taking the matter-of-fact stance and the coach cannot recognize and control himself, he will end up ejected but it is going to be because of his own actions not mine.
I haven't ejected a coach or a player for several seasons. I think the last one was probably due to my own angry attitude... could have been prevented. I'm getting better at calming the situation.
Some people just can't understand reason and at times can't control themselves. They don't deserve to be present... toss 'em. But make sure they have given you adequate reason and that you have maintained your composure/integrity.
Oooh by the way. Never argue with anyone in the crowd. That will incite players and coaches and other fans to elevate the tension. If there is ever a need to eject a fan, I suggest having the coach deal with it - rarely do I have any higher game management than the coach himself.